Atomic and electronic structure of 3$C$-SiC(111)-$(2\sqrt{3}\times2\sqrt{3})$-$R30^\circ$ surface

The theoretical studies and ab initio calculations have been carried out for the first time for atomic and electronic structure of four variants of 3$C$-SiC(111)-$(2\sqrt{3}\times2\sqrt{3})$-$R30^\circ$ surface with Si- terminated surface: initial, relaxed, reconstructed, and relaxed after reconstruction. The surface was simulated in the layered superlattice approximation by a system of thin films (slabs) with a thickness of 12 atomic layers separated by vacuum gaps of $\sim$16 $\mathring{\mathrm{A}}$. In order to close the dangling carbon bonds, the opposite side of the film was complemented with 12 atoms of hydrogen. Ab initio calculations were performed by means of QUANTUM ESPRESSO program based on the density functional theory. It is shown that the reconstruction makes the atomic layers split. Our previous works and experimental data show that these splits are observed at reconstructions of surface (111) in crystals with the sphalerite structure. The band structures of four alternative slabs are calculated and analyzed. Total and layer-by-layer valence electron state densities are calculated for four top layers. It is shown that the real surface has a metallic conductivity.